"use client"; import { useMemo, useState } from "react"; const BIT_DEPTHS = [2, 4, 6, 8, 16] as const; const TOY_LAYER_WEIGHTS = [ 0.91, -0.72, 0.64, -0.58, 0.41, -0.33, 0.28, -0.19, 0.15, -0.11, 0.09, -0.06, 0.04, -0.03, 0.02, -0.01, ] as const; type BitDepth = (typeof BIT_DEPTHS)[number]; type StoredCell = { stored: string; }; function clamp(value: number, min: number, max: number) { return Math.min(max, Math.max(min, value)); } function formatFloat(value: number, decimals = 3) { return value.toFixed(decimals); } function toBfloat16Word(value: number) { const floatView = new Float32Array(1); const intView = new Uint32Array(floatView.buffer); floatView[0] = value; const current = intView[0] ?? 0; const leastSignificantBit = (current >> 16) & 1; const roundingBias = 0x7fff + leastSignificantBit; const rounded = (current + roundingBias) & 0xffff0000; intView[0] = rounded; return { reconstructed: floatView[0] ?? value, word: `0x${(rounded >>> 16).toString(16).padStart(4, "0")}`, }; } function getSharedScale(bitDepth: Exclude) { const maxMagnitude = Math.max( ...TOY_LAYER_WEIGHTS.map((value) => Math.abs(value)), ); const qmax = Math.pow(2, bitDepth - 1) - 1; return { qmax, scale: maxMagnitude / qmax, }; } function quantizeCell(value: number, bitDepth: BitDepth): StoredCell { if (bitDepth === 16) { const bf16 = toBfloat16Word(value); return { stored: bf16.word, }; } const { scale, qmax } = getSharedScale(bitDepth); const stored = clamp(Math.round(value / scale), -qmax, qmax); return { stored: String(stored), }; } export function QuantizationGridExplorer() { const [bitDepthIndex, setBitDepthIndex] = useState(0); const bitDepth = BIT_DEPTHS[bitDepthIndex] ?? BIT_DEPTHS[0]; const scaleSummary = bitDepth === 16 ? null : getSharedScale(bitDepth as Exclude); const cells = useMemo( () => TOY_LAYER_WEIGHTS.map((weight) => quantizeCell(weight, bitDepth)), [bitDepth], ); return (

Toy Layer View

Watch a tiny layer get stored as 16 buckets

Each square below is one toy weight slot. The number shown is the stored bucket value.

setBitDepthIndex(Number(event.target.value))} />

{bitDepth === 16 ? ( <> In BF16, each square stores a 16-bit word instead of a tiny bucket. ) : ( <> Smaller bit depths force more weights into the same few bucket values. Scale = {formatFloat(scaleSummary?.scale ?? 0)} )}

{cells.map((cell, index) => (
W{index} {cell.stored}
))}
); }